Picking a Method for Solving Systems

Front

What is the graphing method for solving systems of equations?

Back

The graphing method involves plotting both equations on a coordinate plane and identifying the point where they intersect, which represents the solution to the system.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is slope-intercept form?

Back

Slope-intercept form is a way of writing linear equations as y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables.

Front

What does it mean for a solution to a system of equations to be valid?

Back

A valid solution makes both equations in the system true when the values are substituted back into the equations.

Front

What is a drawback of the graphing method?

Back

A drawback of the graphing method is that the intersection point may not have integer values, requiring estimation.

Front

When should the substitution method be used?

Back

The substitution method should be used when one equation is already solved for one variable, such as y = 2x.

Front

What is the main advantage of the elimination method?

Back

The elimination method can be more efficient for solving systems with larger coefficients or when the equations are not easily manipulated for substitution.

Front

What does it mean if two equations are dependent?

Back

Two equations are dependent if they represent the same line, meaning they have infinitely many solutions.